The rise and fall rate depends on how big the river is, whether it is well developed and controlled, and geography of the area.
My experience is that smaller rivers seem to move up and down faster. Large rivers like Illinois, Mississippi, and similar rise and fall slower but will have a larger difference between min and max level.
It took over a week for the downpour in the midwest to cause the Illinois river to finally crest in Peoria. It took another week and half to return to normal. Yielding a sustained flood of about a week. This river is a major navigable waterway connecting Lake Michigan and Chicago to the Mississippi (meaning that it is operated by the Army Core of Engineers or some such), and is controlled by several locks and dams. Many of the significant tributaries are also controlled by dams, not much can be done when the whole multi state region is given so much water. The smaller tributaries feeding the river flash flooded overnight, and returned to normal within a day.
I believe the Amazon is mostly unrestricted and will typically rise 30-40ft into its flood plain during the rainy seasons, allowing one to canoe gently through the tree canopy.
Illinois and midwest geography is mostly flat, with about 200ft drop from northwest corner of the state, to the southern most tip. Therefore, the rise and fall is slower since the slope is gentle. Steeper areas can rise and fall much faster.